few_shots: Example:
Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Standard options: 
A. Solve linear equations in one variable.
B. Analyze and solve pairs of simultaneous linear equations.


Thought: The last three rows of the table in the first problem involves solving pairs of simultaneous linear equations. The second word problem can also be represented as two simultaneous linear equations.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001392

8
options: Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
problem_activity: Narrative
The purpose of this Number Talk is to elicit strategies and understandings students have for adding within 100. These understandings help students develop fluency and will be helpful later in this lesson when students add 2 two-digit numbers, with composing a ten, using methods based on place value and the properties of operations.
In this activity, students have an opportunity to look for and make use of structure (MP7) because they decompose addends to make a new ten.
Launch
Display one expression.
“Give me a signal when you have an answer and can explain how you got it.”
1 minute: quiet think time
Activity
Record answers and strategy.
Keep expressions and work displayed.
Repeat with each expression.
Student Facing
Find the value of each expression mentally.
\(7 + 3\)
\(37 + 3\)
\(7 + 8\)
\(57 + 8\)
Student Response
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Activity Synthesis
“How could
\(7 + 3\)
help you solve
\(37 + 3\)
?” (I know 37 is 3 more tens than 7. Since I know
\(3 + 7\)
is 10, I need to add
\(30 +10\)
.)
“How could
\(7 + 3\)
help you solve
\(7 + 8\)
?” (
\(7 + 3 = 10\)
. So far I have added 3 of the 8 and have 5 left.
\(10 + 5 = 15\)
.)
“How could
\(7 + 8\)
help you solve
\(57 + 8\)
?” (Since I know
\(7 + 8 = 15\)
, I can add
\(50 + 15 = 65\)
)


correct_option_index: 2